Keep a few things in mind first (sorry if many of you know this already).
The Bad --
1. Multiplayer/Online ("MP") and Single-player ("SP") are completely separate. You can't use your cars purchased online to practice, qualify, or race in SP Custom Cup. Conversely, you can't practice and qualify *at all* in MP Custom Cup (which is distinct from online Custom Cup).
2. To make matters worse, you cannot tune or upgrade your own cars in MP online races until you have reached a certain XP level, and this act is progressive steps. In other words, you have to actually go race your owned car in races and place decently to gain XP to unlock "tuning packs" as they are called. All these are is the ability to tune six components (gear ratio, differential, front suspension, rear suspension, downforce, and brake bias) in three different increments. The first increment level will cost you from 8-16 XP, the second, from 16-32, and the third, from about 32-64. This is a LOT of racing in your own car. Remember, you have to pay to repair your car (nominal) after every race to get it back to 100%.
3. Once you unlock all of the tuning options, to be able to upgrade the car's parts, you will need a ton of XP to do this also. For instance, Flywheel alone initial upgrade is 15 XP and Engine is 30. There are many other parts you can upgrade. (Remember, in league races, we cannot upgrade parts with cash other than that earned in races, so I'm pretty sure component upgrades will be severely limited). However, it's up to you to buy your car and get as many tuning upgrades to it as possible. You can do that as shown below. Tuning upgrades will not gain you that much time at all, but simply make the car suit either your driving style or the track, which helps, but not nearly as much as practice and skill, since the cars are basically even time wise within each division (but sound wonderfully different and drive differently too).
So...how do you quickly do all of this?
The Good --
It's not that hard actually. I have invested only about 3-6 hours doing the below steps and already have purchased two cars (Endurance and Touring) for the league, and have about 250,000 sitting in the bank. Have probably earned close to 1 Million in game cash. Do this --
1. Go to the online section with a like minded mate.
2. Go to Xbox live session with your friend.
3. You are now in your own lobby. There is a menu on the left. Click on Custom Cup.
4. Click "create race" in any discipline and with any car class. If you do not own any vehicles that we race in the league, simply go to the discipline you would like to buy one in (Endurance or Touring) and choose it. Be sure to pick a car that's stable and not prone to getting loose or too fast. Speed does not matter at this point.
5. Race options -- Choose 5 races in a row. Make them all at the Indianapolis oval for ONE LAP. This is the key. Why? Because rewards in this game have nothing to do with race length.
6. Race Settings -- Make sure you go down the menu and add "very hard" A.I. (you can beat them if you start up front) and turn all aids off, limit the view to cockpit, etc. As far as damage goes, this is your call. I would either turn collisions off (ghosts cars) or leave everything at its hardest setting and be careful (as this will earn you more). Make sure your mate understands that you simply want to stay ahead of the A.I. You do this by drafting with your mate and allowing each other to alternate finishing first or second. Each race takes about one minute and the payout is about 20,000 if you win and 10,000 if you come in second. Your could actually loose money if you damage your car too heavily.
7. Advanced settings -- start the races according to XP level so you will start first, since the A.I. have no XP. Also choose no flashbacks and full damage, etc. Max out the difficulty.
8. You will then go through a series of 5 one lap races and soon get the hand of how to finish up top. Before you know it, you will have loads of cash. When you have enough to buy a league car...go do it. BTW, when you are done with the 5 races, it takes you back to the lobby with the settings exactly the same so you can do it again and again.
9. Be sure to put the maximum amount of the highest level sponsors you can on your car so you will get more cash for high finishes. Then, go back into the lobby as described above and create a race with that car class you now own. Be sure to choose your owned car fro the "choose car" menu on the left. Other cars are clearly marked as loaner vehicles.
10. Now, repeat the racing. In addition to general class XP, you will not be earning XP for that car. This means you will be (in short order) unlocking the ability to tune your car more finely and be earning cash at the same time. At some point, you will get enough XP (64 I think) for that particular car that all tuning options and engine options will be available. But *do not* upgrade your car's parts if you want to use it in the league. Just get the tuning packs (which cost money to unlock once you have earned enough XP). There are three levels to each tuning option.
11. Then, you can go to the SP side of the game and create a Custom Cup race anytime on your own. You can make practice 30 mins. and have full tuning capability (like you do now online). As such, you can optimize the car for your driving style, the particular track, the car, and general performance. You can also have loads of fun against what I think are great A.I.
Good luck!